We propose a new algorithm for the optimization of GGFs based on extensions of Frank-Wolfe algorithms for non-smooth optimization [1]}, [2]}, [3]}. These methods usually optimize smoothed surrogate objective functions, while gradually decreasing a smoothing parameter, and a common smoothing technique uses the Moreau envelope [4]}, [5]}. Our main insight is that the gradient of the Moreau envelope of GGFs can be computed in \(O(n \log n)\)  operations, where \(n\)  is the number of users or items. This result unlocks the use of Frank-Wolfe algorithms with GGFs, allowing us to efficiently find optimal ranking policies while optimizing GGFs.
